C₂×#585×D₅₃ #28297983

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂²⁰

Aliases

direct product

C₂×#585×D₅₃

Splittings

Fitting	C₂×C₅₃×#585 ⋊ C₂
Sylow	C₅₃ ⋊ C₂²×#585

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, cosocle	C₂×C₅₃	C₂⁷
Frattini	C₂	C₂⁶×D₅₃
Fitting	C₂×C₅₃×#585	C₂
socle	C₂²×C₅₃	C₂⁶
hypercenter	C₂×#585	D₅₃
hypocenter	C₅₃	C₂²×#585
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#585

60366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 71
transitive degree	μ_t(G) = 1696

A minimal faithful permutation representation — 7 generators on 71 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(56,59,60,67)(57,63,62,69)(58,66,65,71)(61,68,64,70);(57,62)(61,64)(63,69)(68,70);(58,65)(61,64)(66,71)(68,70);(56,58)(57,61)(59,66)(60,65)(62,64)(63,68)(67,71)(69,70);(56,57)(58,64)(59,63)(60,62)(61,65)(66,70)(67,69)(68,71);(54,55)

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1083459);

C2×#585×D53 #28297983